SOLUTION: Mutt and Jeff need to paint a fence. Mutt can do the job alone 2 hours faster than Jeff. If together they work for 34 hours and finish only 2/3 of the job, how long would Jeff need

Question 400107: Mutt and Jeff need to paint a fence. Mutt can do the job alone 2 hours faster than Jeff. If together they work for 34 hours and finish only 2/3 of the job, how long would Jeff need to do the job alone?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Mutt and Jeff need to paint a fence. Mutt can do the job alone 2 hours faster than Jeff. If together they work for 34 hours and finish only 2/3 the job, how long would Jeff need to do the job alone?
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Mutt DATA:
time = x hr/job ; rate = 1/x job/hr
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Jeff DATA:
time = x+2 hr/job ; rate = 1/(x+2) job/hr
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Together DATA:
time = 34 hr/(2/3)job = 51 hr/job : rate = 1/51 job/hr
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Equation:
rate + rate = together rate
1/x + 1/(x+2) = 1/51
51(x+2) + 51x = x(x+2)
102x+102 = x^2+2x
===
x^2 - 100x - 102 = 0
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I graphed this; x is very close to 102 hr (Mutt's time to do job alone)
Jeff's time to do the job alone is x+2 = 104 hrs

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cheers,
Stan H.
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